Search results for "brownian motion"

Phase transitions in single macromolecules: Loop-stretch transition versus loop adsorption transition in end-grafted polymer chains.

2018

We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter $\varepsilon$, and the other is the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force $F$ applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition, and the mean position of the chain end in the case of the loop-stretch transition. Clo…

Noise-Induced Phase Transitions

2009

Critical behavior of active Brownian particles

2017

We study active Brownian particles as a paradigm for a genuine nonequilibrium phase transition requiring steady driving. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a method based on arguments from finite-size scaling to determine critical points and successfully test it for the two-dimensional (2D) Ising model. Using this method allows us to accurately determine the critical point of two-dimensional active Brownian particles at ${\mathrm{Pe}}_{\text{cr}}=40(2), {\ensuremath{\phi}}_{\text{cr}}=0.597(3)$. Based on this estimate, we study the corresponding critical exponents $\ensuremath{\beta}, \ensuremath{\gamma}/\…

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

2015

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with …

Trajectory Statistics of Confined L\'evy Flights and Boltzmann-type Equilibria

2013

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise, where Langevin representation is absent. In view of the L\'{e}vy noise sensitivity to environmental inhomogeneities, the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Here, we infer pdf $\rho (x,t)$ based on numerical path-wise simulation of the underlying jump-type process. A priori given data are jump transition rates entering the master equation for $\rho (x,t)$ and its target pdf $\rho_*(x)$. To simulate the above processes, we construct a suitable modification of t…

Noise delayed decay of unstable states: theory versus numerical simulations

2004

We study the noise delayed decay of unstable nonequilibrium states in nonlinear dynamical systems within the framework of the overdamped Brownian motion model. We give the exact expressions for the decay times of unstable states for polynomial potential profiles and obtain nonmonotonic behavior of the decay times as a function of the noise intensity for the unstable nonequilibrium states. The analytical results are compared with numerical simulations.

Simulating quantum Brownian motion with single trapped ions

2004

We study the open system dynamics of a harmonic oscillator coupled with an artificially engineered reservoir. We single out the reservoir and system variables governing the passage between Lindblad type and non-Lindblad type dynamics of the reduced system's oscillator. We demonstrate the existence of conditions under which virtual exchanges of energy between system and reservoir take place. We propose to use a single trapped ion coupled to engineered reservoirs in order to simulate quantum Brownian motion.

Lindblad- and non-Lindblad-type dynamics of a quantum Brownian particle

2004

The dynamics of a typical open quantum system, namely a quantum Brownian particle in a harmonic potential, is studied focussing on its non-Markovian regime. Both an analytic approach and a stochastic wave function approach are used to describe the exact time evolution of the system. The border between two very different dynamical regimes, the Lindblad and non-Lindblad regimes, is identified and the relevant physical variables governing the passage from one regime to the other are singled out. The non-Markovian short time dynamics is studied in detail by looking at the mean energy, the squeezing, the Mandel parameter and the Wigner function of the system.

Killing (absorption) versus survival in random motion

2017

We address diffusion processes in a bounded domain, while focusing on somewhat unexplored affinities between the presence of absorbing and/or inaccessible boundaries. For the Brownian motion (L\'{e}vy-stable cases are briefly mentioned) model-independent features are established, of the dynamical law that underlies the short time behavior of these random paths, whose overall life-time is predefined to be long. As a by-product, the limiting regime of a permanent trapping in a domain is obtained. We demonstrate that the adopted conditioning method, involving the so-called Bernstein transition function, works properly also in an unbounded domain, for stochastic processes with killing (Feynman-…

LÉVY FLIGHT SUPERDIFFUSION: AN INTRODUCTION

2008

After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the L\'{e}vy flight superdiffusion as a self-similar L\'{e}vy process. The condition of self-similarity converts the infinitely divisible characteristic function of the L\'{e}vy process into a stable characteristic function of the L\'{e}vy motion. The L\'{e}vy motion generalizes the Brownian motion on the base of the $\alpha$-stable distributions theory and fractional order derivatives. The further development of the idea lies on the generalization of the Langevin equation with a non-Gaussian white noise source and the use of functional approach. Th…